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The Hungarian method is a combinatorial optimization algorithm that solves the assignment problem in polynomial time and which anticipated later primal–dual methods.It was developed and published in 1955 by Harold Kuhn, who gave it the name "Hungarian method" because the algorithm was largely based on the earlier works of two Hungarian mathematicians, Dénes Kőnig and Jenő Egerváry.
This algorithm may yield a non-optimal solution. For example, suppose there are two tasks and two agents with costs as follows: Alice: Task 1 = 1, Task 2 = 2. George: Task 1 = 5, Task 2 = 8. The greedy algorithm would assign Task 1 to Alice and Task 2 to George, for a total cost of 9; but the reverse assignment has a total cost of 7.
Harold William Kuhn (July 29, 1925 – July 2, 2014) was an American mathematician who studied game theory. He won the 1980 John von Neumann Theory Prize jointly with David Gale and Albert W. Tucker .
James Raymond Munkres (born August 18, 1930) is a Professor Emeritus of mathematics at MIT [1] and the author of several texts in the area of topology, including Topology (an undergraduate-level text), Analysis on Manifolds, Elements of Algebraic Topology, and Elementary Differential Topology. He is also the author of Elementary Linear Algebra.
In mathematical optimization, the Karush–Kuhn–Tucker (KKT) conditions, also known as the Kuhn–Tucker conditions, are first derivative tests (sometimes called first-order necessary conditions) for a solution in nonlinear programming to be optimal, provided that some regularity conditions are satisfied.
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It might be worth noting that Kuhn credits Jacobi with having essentially invented the algorithm a century earlier, though the connection wasn't realized until recently. --Delirium 04:51, 13 August 2008 (UTC) In the section "The algorithm in terms of bipartite graphs", the argument for Delta being positive is unsatisfactory.
Since it gained popularity in 2020, TikTok has posed a major competitive threat to Instagram — drawing away users’ attention and time and forcing the older app to rework its algorithm.